Using a small sharp knife, score the flank steak on both sides in a shallow crosshatch pattern and transfer to a shallow baking dish. In a small bowl, combine the soy sauce, lime juice and ginger. Pour 2/3 cup of the soy marinade over the flank steak and turn to coat. Let stand for 10 minutes. Reserve the remaining marinade.

Meanwhile, light a grill or preheat a grill pan. Brush 2 tablespoons of the olive oil over the cut sides of the eggplant and season with salt and pepper.

Remove the steak from the marinade and pat dry. Brush the steak with the remaining 2 tablespoons of olive oil and season with pepper. Grill the steak over moderately high heat, turning occasionally, about 11 minutes for medium to medium-rare meat. Simultaneously, grill the eggplant until tender and browned, 11 minutes. Transfer the steak to a cutting board and let rest for 5 minutes. Thinly slice the meat against the grain. Transfer the meat and eggplant to plates, drizzle with the reserved marinade and serve.